The dihedral angle is the upward angle measured from horizontal of the wings or tailplane of an aircraft. If there are multiple sections of a wing having different angles from horizontal, then the wing can be referred to as polyhedral. Wing dihedral angle is known to play a role in lateral-directional stability. In standard aircraft including almost all large commercial and private aircraft, the wings are typically set at a fixed positive dihedral angle for stability. Aircraft such as the Lockheed Martin F-104 and AV-8B Harrier use a negative dihedral (anhedral) setting for improved agility. These basic aspects have been well-studied, and are covered in many textbooks related to flight. A flexible wing deforms in a way that the effective dihedral of the wing increases. This only adds to the stabilizing effect of the dihedral. The changes resulting from flexibility have also been documented.
Unlike fixed wing aircraft, flapping wing aircraft possess the ability to change the dihedral angle on demand. An asymmetric wing setting naturally produces a yawing moment, however. Others have investigated the use of articulated wings for roll and yaw control. The approach studied has focused on controllable winglets. An example of this type of control is found in various papers published by Friswell, Bourdin et al. See, e.g., Bourdin et al., “Aircraft Control via Variable Cant-Angle Winglets,” Journal of Aircraft, Vol. 45, No. 2, March-April 2008. In this approach, the canted winglet in the inner wing is deflected upward to induce a turn. This reduces the net lift on the inner wing to induce the desired rolling moment, while the upward deflected winglet acts like a vertical tail and produces a proverse yawing moment in response to the rolling moment. This approach requires a segmented wing, and that only the winglet be deflected. With a monolithic wing, this approach can impair turning because the side force from the deflected wing may adversely dominate the side force required for turn (in a right turn, the deflected winglet produces a leftward force, whereas a rightward force is required to sustain/aid the turn).
Prior work by the present inventors and colleagues has advanced the state of micro aerial craft with articulated wings. Paranjape, A. A., Chung, S.-J., and Selig, M. S., “Flight Mechanics of a Tailless Articulated Wing Aircraft,” Bioinspiration & Biomimetics, Vol. 6, No. 2, (12 Apr. 2011) discloses a micro aerial aircraft with articulated wings and a horizontal tail (no vertical “tail”, and thus the reference to “tailless” aircraft in the title). This paper discloses that the wing dihedral can be varied symmetrically, along with the horizontal tail, to control the flight path angle independently of the fight speed. The micro aerial aircraft in the paper used dihedral angles that could be set asymmetrically for executing rapid zero sideslip turns. This work showed that the sign of the yaw moment derivative with respect to anti-symmetric dihedral depends strongly on the angle of attack and the angular rates. The primary demonstration of this work was to show that the yaw control effectiveness of the anti-symmetric dihedral depends primarily on the angle of attack, and also on the angular rates. When the angular rates are zero, the sign of the effectiveness depends on the sign (xaCL/c+Cm,ac), where xa/c is the non-dimensional distance between the center of gravity and the quarter-chord line. Furthermore, Cm,ac<0 for wings with a positive camber, and therefore, at small angles of attack, the control effectiveness is negative and it is positive at higher angles of attack. For an intermediate range of angles of attack, the sign depends on the angular rates as well. This can cause immense problems for yaw control, particularly when the angle of attack varies across the three regions in the course of a maneuver. There was not a solution proposed for these problems in this paper. This unresolved problem had to do with yaw control effectiveness changing its sign inside the routinely flown flight envelope. The sign was seen to be sensitive to the angle of attack as well as the angular rates. Basically, every control law assumes that the sign of control effectiveness is known; if it changes sign inside the envelope and does so as a function of several variables, it is virtually impossible to design a robust, reliable controller. Thus, this paper did not provide a practical solution for a tailless micro aerial aircraft.